Will I know if someone else is bidding on the name I started the auction for? Will I get a chance to counter-bid?

No, you will not know about other bids until the end of 3 day bidding period. After which, all bids will be revealed but you wont be able to raise your bid at that time. If the name is important for you, bid for the max value you are willing to pay, if you are the only bidder, you will only pay the base price, and your additional bid amount will be refunded.